Finite Group Databasebeta

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C32×C7×D11⋊C25 #46831403

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C7×C25 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×D11⋊C25
unambiguous semidirect productD11⋊(C32×C7×C25)
unambiguous semidirect product(C3×D11)⋊(C3×C7×C25)
unambiguous semidirect product(C32×D11)⋊(C7×C25)
unambiguous semidirect product(C11⋊C25)⋊(C2×C32×C7)
unambiguous semidirect product(C32×C7×D11)⋊C25

Splittings

derived, SylowC11 ⋊ C2×C32×C7×C25
HallC32×C7×C11⋊C25 ⋊ C2
HallC32×C11⋊C25 ⋊ C2×C7
HallC7×C11⋊C25 ⋊ C2×C32
HallC32×C7×D11 ⋊ C25
HallC32×C7×C11 ⋊ C2×C25
HallC11⋊C25 ⋊ C2×C32×C7
HallC32×D11 ⋊ C7×C25
HallC7×D11 ⋊ C32×C25
HallC32×C11 ⋊ C2×C7×C25
HallC7×C11 ⋊ C2×C32×C25
HallD11 ⋊ C32×C7×C25

Subgroups

subgroupG/H
center, hypercenterC32×C5×C7AGL(1,𝔽11)
commutator, hypocenterC11C2×C32×C7×C25
FrattiniC5C32×C7×AGL(1,𝔽11)
Fitting, socleC32×C5×C7×C11C2×C5
prime radicalC32×C5×C7×D11C5
cosocleC5×C11C2×C32×C5×C7
LCSG ▷ C11
UCSC1 ◁ C32×C5×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

3465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 46);